{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 19 - Evaluating Causal Models\n",
    "\n",
    "In the vast majority of material about causality, researchers use synthetic data to check if their methods are any good. Much like we did in the When Prediction Fails chapter, they generate data on both $Y_{0i}$ and $Y_{1i}$ so that they can check if their model is correctly capturing the treatment effect $Y_{1i} - Y_{0i}$. That's fine for academic purposes, but in the real world, we don't have that luxury. When applying these techniques in the industry, we'll be asked time and again to prove why our model is better, why should it replace the current one in production or why it won't fail miserably. This is so crucial that it's beyond my comprehension why we don't see any material whatsoever explaining how we should evaluate causal inference models with real data. \n",
    "\n",
    "As a consequence, data scientists that want to apply causal inference models have a really hard time convincing management to trust them. The approach they take is one of showing how sound the theory is and how careful they've been while training the model. Unfortunately, in a world where train-test split paradigm is the norm, that just won't cut it. The quality of your model will have to be grounded on something more concrete than a beautiful theory. Think about it. Machine learning has only achieved its huge success because predictive model validation is very straightforward. There is something reassuring about seeing that the predictions match what really happened. \n",
    "\n",
    "Unfortunately, it isn't obvious at all how we achieve anything like a train-test paradigm in the case of causal inference. That's because causal inference is interested in estimating an unobservable quantity, $\\frac{\\delta y}{ \\delta t}$. Well, if we can't see it, how the hell are we supposed to know if our models are any good at estimating it? Remember, it is as if every entity had an underlying responsiveness, denoted by the slope of the line from treatment to outcome, but we can't measure it.\n",
    "\n",
    "![img](./data/img/evaluate-causal-models/sneak.png)\n",
    "\n",
    "This is a very very very hard thing to wrap our heads around and it took me years to find something close to an answer. Is not a definitive one, but it works in practice and it has that concreteness, which I hope will approach causal inference from a train-test paradigm similar to the one we have with machine learning. The trick is to use aggregate measurements of sensitivity. Even if you can't estimate sensitivity individually, you can do it for a group and that is what we will leverage here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:20.204656Z",
     "start_time": "2023-08-01T11:58:17.756514Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "from toolz import curry\n",
    "\n",
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.api as sm\n",
    "\n",
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this chapter, we'll use non random data to estimate our causal models and random data to evaluate it. Again, we will be talking about how price impacts ice cream sales. As we'll see, random data is very valuable for evaluation purposes. However, in real life, it is often expensive to collect random data (why would you set prices at random if you know some of them are not very good ones and will only make you lose money???). What ends up happening is that we often have an abundance of data where the treatment is **NOT** random and very few, if any, random data. Since evaluating a model with non random data is incredibly tricky, if we have any random data, we  tend to leave that for evaluation purposes. \n",
    "\n",
    "And just in case you forgot, here is what the data looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:20.226280Z",
     "start_time": "2023-08-01T11:58:20.206641Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5000, 5)\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>temp</th>\n",
       "      <th>weekday</th>\n",
       "      <th>cost</th>\n",
       "      <th>price</th>\n",
       "      <th>sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.3</td>\n",
       "      <td>6</td>\n",
       "      <td>1.5</td>\n",
       "      <td>5.6</td>\n",
       "      <td>173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>25.4</td>\n",
       "      <td>3</td>\n",
       "      <td>0.3</td>\n",
       "      <td>4.9</td>\n",
       "      <td>196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>23.3</td>\n",
       "      <td>5</td>\n",
       "      <td>1.5</td>\n",
       "      <td>7.6</td>\n",
       "      <td>207</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>26.9</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3</td>\n",
       "      <td>5.3</td>\n",
       "      <td>241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20.2</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>7.2</td>\n",
       "      <td>227</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   temp  weekday  cost  price  sales\n",
       "0  17.3        6   1.5    5.6    173\n",
       "1  25.4        3   0.3    4.9    196\n",
       "2  23.3        5   1.5    7.6    207\n",
       "3  26.9        1   0.3    5.3    241\n",
       "4  20.2        1   1.0    7.2    227"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices = pd.read_csv(\"./data/ice_cream_sales.csv\") # loads non-random data\n",
    "prices_rnd = pd.read_csv(\"./data/ice_cream_sales_rnd.csv\") # loads random data\n",
    "print(prices_rnd.shape)\n",
    "prices.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To have something to compare, let's train two models. The first one will be a linear regression with interactions terms so that sensitivity is allowed to vary between units. \n",
    "\n",
    "$$\n",
    "sales_i = \\beta_0 + \\beta_1 price_i + \\pmb{\\beta_2 X}_i + \\pmb{\\beta_3 X}_i price_i + e_i\n",
    "$$\n",
    "\n",
    "Once we fit this model, we will be able to make sensitivity predictions\n",
    "\n",
    "$$\n",
    "\\widehat{\\frac{\\delta sales}{ \\delta price}} = \\hat{\\beta_1} + \\pmb{\\hat{\\beta_3} X}_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:20.287386Z",
     "start_time": "2023-08-01T11:58:20.227398Z"
    }
   },
   "outputs": [],
   "source": [
    "m1 = smf.ols(\"sales ~ price*cost + price*C(weekday) + price*temp\", data=prices).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second model will be fully nonparametric, machine learning, predictive model\n",
    "\n",
    "$$\n",
    "sales_i = G(X_i, price_i) + e_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:20.640910Z",
     "start_time": "2023-08-01T11:58:20.288801Z"
    }
   },
   "outputs": [],
   "source": [
    "X = [\"temp\", \"weekday\", \"cost\", \"price\"]\n",
    "y = \"sales\"\n",
    "\n",
    "np.random.seed(1)\n",
    "m2 = GradientBoostingRegressor()\n",
    "m2.fit(prices[X], prices[y]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just to make sure the model is not heavily overfitting, we can check the $R^2$ on the data we've used to train it and on the new, unseen data. (For those more versed in Machine Learning, notice that some drop in performance is expected, because there is a concept drift. The model was trained in data where price is not random, but the test set has only randomized prices)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:20.665750Z",
     "start_time": "2023-08-01T11:58:20.643072Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train Score: 0.9251704824568053\n",
      "Test Score: 0.7711074163447711\n"
     ]
    }
   ],
   "source": [
    "print(\"Train Score:\", m2.score(prices[X], prices[y]))\n",
    "print(\"Test Score:\", m2.score(prices_rnd[X], prices_rnd[y]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After training our models, we will get the sensitivity from the regression model. Again, we will resort to a numerical approximation\n",
    "\n",
    "$$\n",
    "\\frac{\\delta y(t)}{\\delta t} \\approx  \\frac{y(t+h) - y(t)}{h}\n",
    "$$\n",
    "\n",
    "Our models were trained on non-random data. Now we turn to the random data to make predictions. Just so we have everything in one place, we will add the predictions from the machine learning model and the sensitivity prediction from the causal model in a single dataframe, `prices_rnd_pred`.\n",
    "\n",
    "Moreover, let's also include a random model. The idea is that this model just outputs random numbers as predictions. It is obviously not very useful, but it shall serve well as a benchmark. Whenever we are talking about new ways of making evaluations, I always like to think about how a random (useless) model would do. If the random model is able to perform well on the evaluation criterion, that says something about how good the evaluation method really is. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:20.704057Z",
     "start_time": "2023-08-01T11:58:20.666910Z"
    }
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>temp</th>\n",
       "      <th>weekday</th>\n",
       "      <th>cost</th>\n",
       "      <th>price</th>\n",
       "      <th>sales</th>\n",
       "      <th>sensitivity_m_pred</th>\n",
       "      <th>pred_m_pred</th>\n",
       "      <th>rand_m_pred</th>\n",
       "    </tr>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>25.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3</td>\n",
       "      <td>7</td>\n",
       "      <td>230</td>\n",
       "      <td>-13.096964</td>\n",
       "      <td>224.067406</td>\n",
       "      <td>0.696469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>22.7</td>\n",
       "      <td>3</td>\n",
       "      <td>0.5</td>\n",
       "      <td>4</td>\n",
       "      <td>190</td>\n",
       "      <td>1.054695</td>\n",
       "      <td>189.889147</td>\n",
       "      <td>0.286139</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>33.7</td>\n",
       "      <td>7</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5</td>\n",
       "      <td>237</td>\n",
       "      <td>-17.362642</td>\n",
       "      <td>237.255157</td>\n",
       "      <td>0.226851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>23.0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.5</td>\n",
       "      <td>5</td>\n",
       "      <td>193</td>\n",
       "      <td>0.564985</td>\n",
       "      <td>186.688619</td>\n",
       "      <td>0.551315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>24.4</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3</td>\n",
       "      <td>252</td>\n",
       "      <td>-13.717946</td>\n",
       "      <td>250.342203</td>\n",
       "      <td>0.719469</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   temp  weekday  cost  price  sales  sensitivity_m_pred  pred_m_pred  \\\n",
       "0  25.8        1   0.3      7    230          -13.096964   224.067406   \n",
       "1  22.7        3   0.5      4    190            1.054695   189.889147   \n",
       "2  33.7        7   1.0      5    237          -17.362642   237.255157   \n",
       "3  23.0        4   0.5      5    193            0.564985   186.688619   \n",
       "4  24.4        1   1.0      3    252          -13.717946   250.342203   \n",
       "\n",
       "   rand_m_pred  \n",
       "0     0.696469  \n",
       "1     0.286139  \n",
       "2     0.226851  \n",
       "3     0.551315  \n",
       "4     0.719469  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def predict_sensitivity(model, price_df, h=0.01):\n",
    "    return (model.predict(price_df.assign(price=price_df[\"price\"]+h))\n",
    "            - model.predict(price_df)) / h\n",
    "\n",
    "np.random.seed(123)\n",
    "prices_rnd_pred = prices_rnd.assign(**{\n",
    "    \"sensitivity_m_pred\": predict_sensitivity(m1, prices_rnd), ## sensitivity model\n",
    "    \"pred_m_pred\": m2.predict(prices_rnd[X]), ## predictive model\n",
    "    \"rand_m_pred\": np.random.uniform(size=prices_rnd.shape[0]), ## random model\n",
    "})\n",
    "\n",
    "prices_rnd_pred.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sensitivity by Model Band\n",
    "\n",
    "Now that we have our predictions, we need to evaluate how good they are. And remember, we can't observe sensitivity, so there isn't a simple ground truth we can compare against. Instead, let's think back to what we want from our sensitivity models. Perhaps that will give us some insights into how we should evaluate them. \n",
    "\n",
    "The idea of making treatment sensitivity models came from the necessity of finding which units are more sensitive to the treatment and which are less. It came from a desire for personalisation. Maybe a marketing campaign is very effective in only one segment of the population. Maybe discounts only work for some type of customers. A good causal model should help us find which customers will respond better and worse to a proposed treatment. They should be able to separate units into how elastic or sensitive they are to the treatment. In our ice cream example, the model should be able to figure out in which days are people willing to spend more on ice cream or, in which days is the price sensitivity less negative. \n",
    "\n",
    "If that is the goal, it would be very useful if we could somehow order units from more sensitive to less sensitive. Since we have the predicted sensitivity, we can order the units by that prediction and hope it also orders them by the real sensitivity. Sadly, we can't evaluate that ordering on a unit level. But, what if we don't need to? What if, instead, we evaluate groups defined by the ordering? If our treatment is randomly distributed (and here is where randomness enters), estimating sensitivity for a group of units is easy. All we need is to compare the outcome between the treated and untreated.\n",
    "\n",
    "To understand this better, it's useful to picture the binary treatment case. Let's keep the pricing example, but now the treatment is a discount. In other words, prices can be either high (untreated) or low (treated). Let's plot sales on the Y axis, each of our models in the X axis and price as the color. Then, we can split the data on the model axis into three equal sized groups. **If the treatment was randomly assigned**, we can easily estimate the ATE for each group $E[Y|T=1] - E[Y|T=0]\n",
    "$.\n",
    "\n",
    "![img](./data/img/evaluate-causal-models/ate_bins.png)\n",
    "\n",
    "In the image, we can see that the first model is somewhat good at predicting sales (high correlation with sales), but the groups it produces have roughly the same treatment effect, as shown in the plot on the bottom. Two of the three segments have the same sensitivity and only the last one has a different, lower sensitivity.\n",
    "\n",
    "On the other hand, each group produced by the second model has a different causal effect. That's a sign this model can indeed be useful for personalisation. Finally, the random model produces groups with the exact same sensitivity. That's not very useful, but it's expected. If the model is random, each segment it produces will be a random and representative sample of the data. So the sensitivity in its groups should be roughly the same as the ATE on the entire dataset.\n",
    "\n",
    "Just by looking at these plots, you can get a feeling of which model is better. The more ordered the sensitivities look like and the more different they are between bands, the better. Here, model 2 is probably better than model 1, which is probably better than the random model.\n",
    "\n",
    "To generalize this to the continuous case, we can estimate the sensitivity using a single variable linear regression model. \n",
    "\n",
    "$$\n",
    "y_i = \\beta_0 + \\beta_1t_i + e_i\n",
    "$$\n",
    "\n",
    "If we run that model with the sample from a group, we will be estimating the sensitivity inside that group. \n",
    "\n",
    "From the theory on simple linear regression, we know that\n",
    "\n",
    "$$\n",
    "\\hat{\\beta_1}=\\dfrac{\\sum (t_i - \\bar{t}) (y_i - \\bar{y})}{\\sum(t_i - \\bar{t})^2}\n",
    "$$\n",
    "\n",
    "where $\\bar{t}$ is the sample average for the treatment and $\\bar{y}$ is the sample average for the outcome. Here is what that looks like in code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:20.708455Z",
     "start_time": "2023-08-01T11:58:20.705650Z"
    }
   },
   "outputs": [],
   "source": [
    "@curry\n",
    "def sensitivity(data, y, t):\n",
    "        # line coeficient for the one variable linear regression \n",
    "        return (np.sum((data[t] - data[t].mean())*(data[y] - data[y].mean())) /\n",
    "                np.sum((data[t] - data[t].mean())**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now apply this to our ice cream price data. For that, we also need a function that segments the dataset into partitions of equal size and applies the sensitivity to each partition. The following code should handle that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:20.712974Z",
     "start_time": "2023-08-01T11:58:20.710002Z"
    }
   },
   "outputs": [],
   "source": [
    "def sensitivity_by_band(df, pred, y, t, bands=10):\n",
    "    return (df\n",
    "            .assign(**{f\"{pred}_band\":pd.qcut(df[pred], q=bands)}) # makes quantile partitions\n",
    "            .groupby(f\"{pred}_band\")\n",
    "            .apply(sensitivity(y=y, t=t))) # estimate the sensitivity on each partition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's plot the sensitivity by band using the predictions we've made before. Here, we will use each model to construct partitions and then estimate the sensitivity on each partition. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:21.032673Z",
     "start_time": "2023-08-01T11:58:20.714440Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3, sharey=True, figsize=(10, 4))\n",
    "for m, ax in zip([\"sensitivity_m_pred\", \"pred_m_pred\", \"rand_m_pred\"], axs):\n",
    "    sensitivity_by_band(prices_rnd_pred, m, \"sales\", \"price\").plot.bar(ax=ax)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, look at the random model (`rand_m`). It has roughly the same estimated sensitivity in each of its partitions. We can already see just by looking at the plot that it won't help us much with personalisation since it can't distinguish between the high and low price sensitivity days. Next, consider the predictive model, `pred_m`. That model is actually promising! It manages to construct groups where the sensitivity is high and others where the sensitivity is low. That's exactly what we need. \n",
    "\n",
    "Finally, the causal model `sensitivity_m` looks a bit weird. It identifies groups of really low sensitivity, where low here actually means high price sensitivity (sales will decrease by a lot as we increase prices). Detecting those high price sensitivity days is very useful for us. If we know when they are, we will be careful not to go on increasing prices on those types of days. The causal model also identifies some less sensitive regions, so it can successfully distinguish high from low sensitivities. But the ordering is not as good as that of the predictive model. \n",
    "\n",
    "So, what should we decide? Which one is more useful? The predictive or the causal model? The predictive model has better ordering, but the causal model can better identify the extremes. The sensitivity by band plot is a good first check, but it can't answer precisely which model is better. We need to move to something more elaborate.\n",
    "\n",
    "## Cumulative Sensitivity Curve\n",
    "\n",
    "Consider again the illustrative example where price was converted to a binary treatment. We will take it from where we left, so we had the sensitivity of the treatment by band. What we can do next is order the band according to how sensitive they are. That is, we take the most sensitive group and place it in the first place, the second most sensitive group in the second place and so on. For both models 1 and 3, no re-ordering needs to be made, since they are already ordered. For model 2, we have to reverse the ordering. \n",
    "\n",
    "Once we have the ordered groups, we can construct what we will call the Cumulative Sensitivity Curve. We first compute the sensitivity of the first group; then, of the first and the second and so on, until we've included all the groups. In the end, we will just compute the sensitivity for the entire dataset. Here is what it would look like for our illustrative example.\n",
    "\n",
    "![img](./data/img/evaluate-causal-models/cumm_elast.png)\n",
    "\n",
    "Notice that the first bin in the cumulative sensitivity is just the ATE from the most sensitive group according to that model. Also, for all models, the cumulative sensitivity will converge to the same point, which is the ATE for the entire dataset. \n",
    "\n",
    "Mathematically, we can define the cumulative sensitivity as the sensitivity estimated up until unit $k$. \n",
    "\n",
    "$$\n",
    "\\widehat{y'(t)}_k = \\hat{\\beta_1}_k=\\dfrac{\\sum_i^k (t_i - \\bar{t}) (y_i - \\bar{y})}{\\sum_i^k(t_i - \\bar{t})^2}\n",
    "$$\n",
    "\n",
    "To build the cumulative sensitivity curve, we run the above function iteratively in the dataset to produce the following sequence. \n",
    "\n",
    "$$\n",
    "(\\widehat{y'(t)}_1, \\widehat{y'(t)}_2, \\widehat{y'(t)}_3,..., \\widehat{y'(t)}_N)\n",
    "$$\n",
    "\n",
    "This is a very interesting sequence in terms of model evaluation because we can make preferences statements about it. First, a model is better to the degree that\n",
    "\n",
    "$\\hat{y}'(t)_k > \\hat{y}'(t)_{k+a}$\n",
    "\n",
    "for any $k$ and $a>0$. In words, if a model is good at ordering sensitivity, the sensitivity observed in the top $k$ samples should be higher than the sensitivity observed in top $k+a$ samples. Or, simply put, if I look at the top units, they should have higher sensitivity than units below them. \n",
    "\n",
    "Second, a model is better to the degree that \n",
    "\n",
    "$\\hat{y}'(t)_k - \\hat{y}'(t)_{k+a}$\n",
    "\n",
    "is the largest, for any $k$ and $a>0$. The intuition being that not only do we want the sensitivity of the top $k$ units to be higher than the sensitivity of the units below them, but we want that difference to be as large as possible. \n",
    "\n",
    "To make it more concrete, here is this idea represented in code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:21.036928Z",
     "start_time": "2023-08-01T11:58:21.033995Z"
    }
   },
   "outputs": [],
   "source": [
    "def cumulative_sensitivity_curve(dataset, prediction, y, t, min_periods=30, steps=100):\n",
    "    size = dataset.shape[0]\n",
    "    \n",
    "    # orders the dataset by the `prediction` column\n",
    "    ordered_df = dataset.sort_values(prediction, ascending=False).reset_index(drop=True)\n",
    "    \n",
    "    # create a sequence of row numbers that will define our Ks\n",
    "    # The last item is the sequence is all the rows (the size of the dataset)\n",
    "    n_rows = list(range(min_periods, size, size // steps)) + [size]\n",
    "    \n",
    "    # cumulative computes the sensitivity. First for the top min_periods units.\n",
    "    # then for the top (min_periods + step*1), then (min_periods + step*2) and so on\n",
    "    return np.array([sensitivity(ordered_df.head(rows), y, t) for rows in n_rows])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some things to notice about this function. It assumes that the thing which ordered the sensitivity is stored in the column passed to the `prediction` argument. Also, the first group has `min_periods` units, so it can be different from the others. The reason is that, due to small sample size, the sensitivity can be too noisy at the beginning of the curve. To fix that, we can pass a first group which is already large enough. Finally, the `steps` argument defines how many extra units we include in each subsequent group.   \n",
    "\n",
    "With this function, we can now plot the cumulative sensitivity curve, according to the ordering produced by each of our models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:21.283989Z",
     "start_time": "2023-08-01T11:58:21.038649Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "\n",
    "for m in [\"sensitivity_m_pred\", \"pred_m_pred\", \"rand_m_pred\"]:\n",
    "    cumu_sens = cumulative_sensitivity_curve(prices_rnd_pred, m, \"sales\", \"price\", min_periods=100, steps=100)\n",
    "    x = np.array(range(len(cumu_sens)))\n",
    "    plt.plot(x/x.max(), cumu_sens, label=m)\n",
    "\n",
    "plt.hlines(sensitivity(prices_rnd_pred, \"sales\", \"price\"), 0, 1, linestyles=\"--\", color=\"black\", label=\"Avg. Sens.\")\n",
    "plt.xlabel(\"% of Top Sensitivity. Days\")\n",
    "plt.ylabel(\"Cumulative Sensitivity\")\n",
    "plt.title(\"Cumulative Sensitivity Curve\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interpreting a Cumulative Sensitivity Curve can be a bit challenging, but here is how I see it. Again, it might be easier to think about the binary case. The X axis of the curve represents how many samples are we treating. Here, I've normalized the axis to be the proportion of the dataset, so .4 means we are treating 40% of the samples. The Y axis is the sensitivity we should expect at that many samples. So, if a curve has value -1 at 40%, it means that the sensitivity of the top 40% units is -1. Ideally, we want the highest sensitivity for the largest  possible sample. An ideal curve then would start high up on the Y axis and descend very slowly to the average sensitivity, representing we can treat a high percentage of units while still maintaining an above average sensitivity. \n",
    "\n",
    "Needless to say, none of our models gets even close to an ideal sensitivity curve. The random model `rand_m` oscillates around the average sensitivity and never goes too far away from it. This means that the model can't find groups where the sensitivity is different from the average one. As for the predictive model `pred_m`, it appears to be reversely ordering sensitivity, because the curve starts below the average sensitivity. Not only that, it also converges to the average sensitivity pretty quickly, at around 50% of the samples. Finally, the causal model `sensitivity_m` seems more interesting. It has this weird behavior at first, where the cumulative sensitivity increases away from the average, but then it reaches a point where we can treat about 75% of the units while keeping a pretty decent sensitivity of almost 0. This is probably happening because this model can identify the very low sensitivity (high price sensitivity) days. Hence, provided we don't increase prices on those days, we are allowed to do it for most of the sample (about 75%), while still having a low price sensitivity. \n",
    "\n",
    "In terms of model evaluation, the Cumulative Sensitivity Curve is already much better than the simple idea of sensitivity by band. Here, we managed to make preference statements about our models that were much more precise. Still, it's a complicated curve to understand. For this reason, we can do one further improvement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cumulative Gain Curve\n",
    "\n",
    "The next idea is a very simple, yet powerful improvement on top of the cumulative sensitivity. We will multiply the cumulative sensitivity by the proportional sample size. For example, if the cumulative sensitivity is, say -0.5 at 40%, we will end up with -0.2 (-0.5 * 0.4)  at that point. Then, we will compare this with the theoretical curve produced by a random model. This curve will actually be a straight line from 0 to the average treatment effect. Think about it this way: every point in the cumulative sensitivity of a random model is the ATE, because the model just produces random representative partitions of the data. If at each point along the (0,1) line we multiply the ATE by that point, we will end up with a straight line between zero and the ATE.\n",
    "\n",
    "![img](./data/img/evaluate-causal-models/cumm_gain.png)\n",
    "\n",
    "Once we have the theoretic random curve, we can use it as a benchmark and compare our other models against it. All curves will start and end at the same point. However, the better the model at ordering sensitivity, the more the curve will diverge from the random line in the points between zero and one. For example, in the image above, M2 is better than M1 because it diverges more before reaching the ATE at the end point. For those familiar with the ROC curve, you can think about Cumulative Gain as the ROC for causal models. \n",
    "\n",
    "Mathematically speaking, \n",
    "\n",
    "$$\n",
    "\\widehat{F(t)}_k = \\hat{\\beta_1}_k * \\frac{k}{N} =\\dfrac{\\sum_i^k (t_i - \\bar{t}) (y_i - \\bar{y})}{\\sum_i^k(t_i - \\bar{t})^2} * \\frac{k}{N}\n",
    "$$\n",
    "\n",
    "\n",
    "To implement it in code, all we have to do is add the proportional sample size normalization. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:21.289141Z",
     "start_time": "2023-08-01T11:58:21.285652Z"
    }
   },
   "outputs": [],
   "source": [
    "def cumulative_gain(dataset, prediction, y, t, min_periods=30, steps=100):\n",
    "    size = dataset.shape[0]\n",
    "    ordered_df = dataset.sort_values(prediction, ascending=False).reset_index(drop=True)\n",
    "    n_rows = list(range(min_periods, size, size // steps)) + [size]\n",
    "    \n",
    "    ## add (rows/size) as a normalizer. \n",
    "    return np.array([sensitivity(ordered_df.head(rows), y, t) * (rows/size) for rows in n_rows])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For our ice cream data, we will get the following curves. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:21.533445Z",
     "start_time": "2023-08-01T11:58:21.290505Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "\n",
    "for m in [\"sensitivity_m_pred\", \"pred_m_pred\", \"rand_m_pred\"]:\n",
    "    cumu_gain = cumulative_gain(prices_rnd_pred, m, \"sales\", \"price\", min_periods=50, steps=100)\n",
    "    x = np.array(range(len(cumu_gain)))\n",
    "    plt.plot(x/x.max(), cumu_gain, label=m)\n",
    "    \n",
    "plt.plot([0, 1], [0, sensitivity(prices_rnd_pred, \"sales\", \"price\")], linestyle=\"--\", label=\"Random Model\", color=\"black\")\n",
    "\n",
    "plt.xlabel(\"% of Top Sensitivity Days\")\n",
    "plt.ylabel(\"Cumulative Gain\")\n",
    "plt.title(\"Cumulative Gain\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now it is very clear that the causal model (`sensitivity_m`) is much better than the other two. It diverges much more from the random line than both `rand_m` and `pred_m`. Also, notice how the actual random model follows very closely the theoretical random model. The difference between both is probably just random noise. \n",
    "\n",
    "With that, we covered some really nice ideas on how to evaluate causal models. That alone is a huge deed. We managed to evaluate how good are models in ordering sensitivity even though we didn't have a ground truth to compare against. There is only one final thing missing, which to include a confidence interval around those measurements. After all, we are not barbarians, are we?\n",
    "\n",
    "![img](./data/img/evaluate-causal-models/uncivilised.png)\n",
    "\n",
    "\n",
    "## Taking Variance Into Account\n",
    "\n",
    "It just feels wrong to not take variance into account when we are dealing with the sensitivity curves. Specially since all of them use linear regression theory, so adding a confidence interval around them should be fairly easy.\n",
    "\n",
    "To achieve that, we will first create a function that returns the CI for a linear regression parameter. I'm using the formula for the simple linear regression here, but feel free to extract the CI however you want.\n",
    "\n",
    "$$\n",
    "s_{\\hat\\beta_1}=\\sqrt{\\frac{\\sum_i\\hat\\epsilon_i^2}{(n-2)\\sum_i(t_i-\\bar t)^2}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:21.541047Z",
     "start_time": "2023-08-01T11:58:21.537793Z"
    }
   },
   "outputs": [],
   "source": [
    "def sensitivity_ci(df, y, t, z=1.96):\n",
    "    n = df.shape[0]\n",
    "    t_bar = df[t].mean()\n",
    "    beta1 = sensitivity(df, y, t)\n",
    "    beta0 = df[y].mean() - beta1 * t_bar\n",
    "    e = df[y] - (beta0 + beta1*df[t])\n",
    "    se = np.sqrt(((1/(n-2))*np.sum(e**2))/np.sum((df[t]-t_bar)**2))\n",
    "    return np.array([beta1 - z*se, beta1 + z*se])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With some minor modification on our `cumulative_sensitivity_curve` function, we can output the confidence interval for the sensitivity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:21.545365Z",
     "start_time": "2023-08-01T11:58:21.542449Z"
    }
   },
   "outputs": [],
   "source": [
    "def cumulative_sensitivity_curve_ci(dataset, prediction, y, t, min_periods=30, steps=100):\n",
    "    size = dataset.shape[0]\n",
    "    ordered_df = dataset.sort_values(prediction, ascending=False).reset_index(drop=True)\n",
    "    n_rows = list(range(min_periods, size, size // steps)) + [size]\n",
    "    \n",
    "    # just replacing a call to `sensitivity` by a call to `sensitivity_ci`\n",
    "    return np.array([sensitivity_ci(ordered_df.head(rows), y, t)  for rows in n_rows])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally, here is the cumulative sensitivity curve with the 95% CI for the causal model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:21.855543Z",
     "start_time": "2023-08-01T11:58:21.546711Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "\n",
    "cumu_gain_ci = cumulative_sensitivity_curve_ci(prices_rnd_pred, \"sensitivity_m_pred\", \"sales\", \"price\", min_periods=50, steps=200)\n",
    "x = np.array(range(len(cumu_gain_ci)))\n",
    "plt.plot(x/x.max(), cumu_gain_ci, color=\"C0\")\n",
    "\n",
    "plt.hlines(sensitivity(prices_rnd_pred, \"sales\", \"price\"), 0, 1, linestyles=\"--\", color=\"black\", label=\"Avg. Sens.\")\n",
    "\n",
    "plt.xlabel(\"% of Top Sens. Days\")\n",
    "plt.ylabel(\"Cumulative Sensitivity\")\n",
    "plt.title(\"Cumulative Sensitivity for sensitivity_m_pred with 95% CI\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the CI gets smaller and smaller as we accumulate more of the dataset. That's because the sample size increases. \n",
    "\n",
    "As for the Cumulative Gain curve, it is also equally simple to get the CI. Again, we just replace a call to the `sensitivity` function with a call to the `sensitivity_ci` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:21.860255Z",
     "start_time": "2023-08-01T11:58:21.857108Z"
    }
   },
   "outputs": [],
   "source": [
    "def cumulative_gain_ci(dataset, prediction, y, t, min_periods=30, steps=100):\n",
    "    size = dataset.shape[0]\n",
    "    ordered_df = dataset.sort_values(prediction, ascending=False).reset_index(drop=True)\n",
    "    n_rows = list(range(min_periods, size, size // steps)) + [size]\n",
    "    return np.array([sensitivity_ci(ordered_df.head(rows), y, t) * (rows/size) for rows in n_rows])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is what it looks like for the causal model. Notice that now, the CI starts small, even though the sample size is smaller at the beginning of the curve. The reason is that the normalization factor $\\frac{k}{N}$ shrinks the ATE parameter and it's CI along with it. Since this curve should be used to compare models, this shouldn't be a problem, as the curve will apply this shrinking factor equally to all the models being evaluated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-01T11:58:22.143148Z",
     "start_time": "2023-08-01T11:58:21.861696Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "\n",
    "cumu_gain = cumulative_gain_ci(prices_rnd_pred, \"sensitivity_m_pred\", \"sales\", \"price\", min_periods=50, steps=200)\n",
    "x = np.array(range(len(cumu_gain)))\n",
    "plt.plot(x/x.max(), cumu_gain, color=\"C0\")\n",
    "\n",
    "plt.plot([0, 1], [0, sensitivity(prices_rnd_pred, \"sales\", \"price\")], linestyle=\"--\", label=\"Random Model\", color=\"black\")\n",
    "\n",
    "plt.xlabel(\"% of Top Sensitivity Days\")\n",
    "plt.ylabel(\"Cumulative Gain\")\n",
    "plt.title(\"Cumulative Gain for sensitivity_m_pred with 95% CI\")\n",
    "plt.legend();"
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    "## Key Ideas\n",
    "\n",
    "Here we saw three ways to check how good a model is in terms of ordering sensitivity. We used these methods as a way to compare and decide between models that have a causal purpose. That's a huge deal. We've managed to check if a model is good at identifying groups with different sensitivities even without being able to see sensitivity!\n",
    "\n",
    "Here, we relied heavily on random data. We trained the model on non-random data, but all the evaluation was done on a sample where the treatment has been randomized. That's because we need some way of confidently estimating sensitivity. Without random data, the simple formulas we used here wouldn't work. As we know very well by now, simple linear regression has omitted variable bias in the presence of confounding variables. \n",
    "\n",
    "Nonetheless, if we can get our hands on some random data, we already know how to compare random models. In the next chapter, we will address the problem of non random data, but before we go, I wanted to say some last words about model evaluation. \n",
    "\n",
    "Let's reiterate how important trustworthy model evaluation is. With the cumulative gain curve, we finally have a good way of comparing models that are used for causal inference. We can now decide which model is better for treatment personalisation. That's a major deal. Most materials you will find out there in causal inference don't give us a good way of doing model evaluation. In my opinion, that's the missing piece we need to make causal inference as popular as machine learning. With good evaluation, we can take causal inference closer to the train-test paradigm that has already been so useful for predictive models. That's a bold statement. Which means I'm careful when I say it, but until now, I haven't found any good criticism of it. If you have some, please let me know.\n",
    "\n",
    "## References \n",
    "\n",
    "The things I've written here are mostly stuff from my head. I've learned them through experience. This means that they have **not** passed the academic scrutiny that good science often goes through. Instead, notice how I'm talking about things that work in practice, but I don't spend too much time explaining why that is the case. It's a sort of science from the streets, if you will. However, I am putting this up for public scrutiny, so, by all means, if you find something preposterous, open an issue and I'll address it to the best of my efforts.\n",
    "\n",
    "I got the ideas from this chapter from a Pierre Gutierrez and Jean-Yves G'erardy's article called *Causal Inference and Uplift Modeling A review of the literature*. The authors explain the concept of a Qini curve. If you search that, you will find it's a technique used for uplift modeling, which you can think of as causal inference for when the treatment is binary. Here, I took the idea from a Qini curve and generalized it to the continuous treatment case. I think the methods presented here work for both continuous and binary cases, but then again, I've never seen them anywhere else, so keep that in mind. \n",
    "\n",
    "I also strongly recommend reading the article by Leo Breiman (2001) on the train-test paradigm: Statistical Modeling: The Two Cultures. It's a great resource if you want to understand what makes a statistical technique successful. \n",
    "\n",
    "## Contribute\n",
    "\n",
    "Causal Inference for the Brave and True is an open-source material on causal inference, the statistics of science. It uses only free software, based in Python. Its goal is to be accessible monetarily and intellectually.\n",
    "If you found this book valuable and you want to support it, please go to [Patreon](https://www.patreon.com/causal_inference_for_the_brave_and_true). If you are not ready to contribute financially, you can also help by fixing typos, suggesting edits or giving feedback on passages you didn't understand. Just go to the book's repository and [open an issue](https://github.com/matheusfacure/python-causality-handbook/issues). Finally, if you liked this content, please share it with others who might find it useful and give it a [star on GitHub](https://github.com/matheusfacure/python-causality-handbook/stargazers)."
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